Inductive sensors are based typically on an alteration of one or more characteristic values of a system of one or more inductive components by virtue of a measurable quantity. Inductive components of such a type may include, for instance, coil, winding or inductor.
The following enter into consideration in particular as characteristic values:                self-inductance L, also called inductance for short,        loss resistance R, which is composed of an ohmic resistance of the winding and other loss contributions,        complex impedance Z=jωL+R with the imaginary unit j and with the angular frequency ω,        loss angle δ=arctan(Re{Z}/Im{Z}),        and also, particularly in the case of magnetic coupling between several components, mutual inductance M. The mutual inductance M can, amongst other things, be measured indirectly as induced voltage in one conductor as a response to a known current in another conductor.        
Measurable quantities that bring about the alteration of the characteristic values may be, amongst other things, position or length, angle, force, pressure or torque. By way of application, a position sensor for the brake pedal of an automobile may be mentioned in exemplary manner.
For inductive sensors, two main approaches in terms of circuit engineering exist, in particular, in the state of the art in order to undertake an electrical measurement of the characteristic values:
One approach is a resonant system. The inductive sensor with its variable characteristic value, usually the inductance L, is part of the frequency-determining network of an oscillator. The oscillator always oscillates at its natural frequency, the most important influencing factor of which is L. The measurement of L has consequently been reduced to a frequency measurement which, for example, can be easily undertaken by counting the periods or zero crossings of the oscillation of the oscillator.
The other approach is a lock-in amplifier (also phase-sensitive rectifier, synchronous demodulator or carrier-frequency amplifier). The inductive sensor receives a stimulus having a fixed frequency (current or voltage). A signal-processing circuit measures the respective other electrical quantity on the basis of the impedance (voltage or current). The processing of the signal corresponds to a narrowband filtering of this quantity around the frequency of the stimulus with subsequent determination of the complex amplitude and formation of a quotient with the stimulus for the purpose of determining the characteristic value. These functions can optionally be realized with analog electronics or largely with the means of digital signal processing and software.
Both approaches have varying disadvantages.
The resonant system has limitations in connection with the layout of the inductive system, because only one oscillation per oscillator is possible. Several signals can be obtained only with several independent oscillators and inductive systems, as a result of which the effort for sensors with ratiometric or differential measurement is distinctly increased. Furthermore, the inductive system always exhibits frequency dependencies—that is to say, it can only be optimally designed for one frequency; the frequency range of the oscillator is always a compromise. Via the change of the oscillation frequency, cross-sensitivities may falsify the result of measurement, because, for instance, in addition to the sensitivity to the measurable quantity, the inductance L is influenced by a further frequency-dependent quantity. Finally, the difference between the maximal and the minimal counting result of the frequency measurement has to exceed a minimum value, in order that the respective requirements with respect to measurement accuracy and resolution are achieved. Depending upon the frequency, a minimal measuring-time is required for this, which under certain circumstances is simply not available.
The lock-in amplifier, on the other hand, operates at a constant frequency but also requires a stimulus at this frequency. The frequency of these forced oscillations can be chosen freely, but by reason of the frequency dependence of the inductive system this constitutes a contradiction to operation in resonance—that is to say, with oscillations at the natural frequency. Therefore the following advantages of resonance cannot be utilized. The inductive system, operated as a resonator, already constitutes a filter, in that at its natural frequency it is able to achieve a particularly high amplitude which facilitates the measurement. Interferences having a frequency that deviates distinctly from this frequency are suppressed by the filter action. Furthermore, in resonance the power requirement of the inductive system for maintaining the oscillation is lowest, if all other parameters remain the same. At a given power of the stimulus, a particularly high amplitude is consequently possible. Of course, these two advantages represent the same state of affairs, in one case from the point of view of the measurement, and in the other case from the point of view of the stimulus.